Precession angular velocity

Note that the angle 6 is small and 1 and co regarding both axes, z and z, are approximately same. It can be seen that the precession angular velocity cOg is higher, the lower the gyro-... 

The solution of this equation is a precession of the vector M around H0 with an angular velocity equilibrium value. In order to explain how the spins approach their equilibrium distribution we must take account of the interactions of the spins among themselves and with the other degrees of freedom of the system. The simplest phenomenological description of the approach to equilibrium of an assembly of magnetic moments, placed in a constant field H0, is given by the equations... 

It is possible to translate these, in three dimensions, as the motion of a magnet of moment p in an applied magnetic field. The magnet axis becomes inclined to the field, precesses around it, and is defined as the Lamour precession. The half-apex angle of the cone equals 0 and the angular velocity is yBo, so that one finds equation 3.16 now rewritten as equation 3.20 ... 

The prime indicates that one has switched to the so-called rotating frame in order to remove any precession effect at the angular velocity coq = 2tivo, Vo being the resonance frequency. 

The interaction of a nucleus with the oscillating magnetic field B0, created by the electromagnetic wave, can be understood if it is assumed that it results from the composition of two half vectors, rotating in opposite directions in the xOy plane with identical angular velocities (Fig. 9.6). The vector rotating in the same direction as the precession is the only one that can interact with the nucleus. 

Let l = 0. Then a dipole librates in a plane comprising the symmetry axis. Then in view of Eqs. (42a) and (42b) the effective potential w coincides with a true potential. It follows from Eq. (43) that precession is lacking,14 and the angular velocity vj/ = 0. 

Let the distribution Pb(0, excited state (see Fig. 4.1(6)) arise under the action of light in the form of a short pulse (6-pulse). The magnetic field B creates precession around B not only of the angular momentum of a separate molecule, but also of the distribution over the ensemble. Since, however, all momenta J are in precession with one and the same angular velocity ujj (4.2), their mutual positions with respect to each other remain the same. Hence, the whole rose of vectors J is in precession as a single entity, which means that the... 

It cannot be emphasized too much that the resonant frequency in NMR is proportional to the magnetogyric ratio, y, and to the laboratory magnetic field strength, B0. This relationship forms the basis of nearly every phenomenon observed in NMR. There are two ways to measure the precession rate the angular velocity, co0, in units of radians per second and the frequency, v0, in units of cycles per second or hertz. In this book we will use frequencies in hertz. This frequency is sometimes called the Larmor frequency, and the zero subscript refers to this fundamental frequency, which results from the laboratory magnetic field interacting with the nucleus magnetic field. 

The precession frequency, also called the Larmor frequency, is represented as v0 ( new-zero, in hertz or cycles per second). The division by In is sometimes omitted because the units of y can be expressed in hertz per tesla rather than radians per seconds per tesla. When the Larmor frequency is represented in units of radians per second it is called the angular velocity or co0. These are related by a factor of In ... 

These simple product operators precess in the x -y plane of the rotating frame at a frequency corresponding to the chemical shift in hertz relative to the center of the spectral window (the resonance offset Av = v0 — vr). The chemical shift frequency Av can also be represented as the angular velocity 2 in units of rad/s ( 2 = 2ttAv). Using 2 allows us to skip all the 2tt terms. 

Two protons will precess at the same angular velocity only when the magnetic field strengths at their nuclei are the same. In any situation of chemical interest they are bonded to other species, and the applied magnetic field is shielded to some extent by the bonding electrons and further modified by the other charged parts of the molecule. In a molecule containing two or more non-equivalent protons, the NMR peaks do not come at the same place and the difference between the two positions or their positions relative to a standard—the chemical shift 5— is of in-... 

This implies that m evolves such that its modulus is constant, maintaining a constant angle with the direction of B. This motion is called precession. The angular velocity of this precession is u> = yB. 

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